CHAPTER 2: OPTIMAL PIPE DIAMETER FOR A
SINGLE PIPE SEGMENT
To find the optimal diameter for a single pair of supply and return pipes, we need
to consider the costs involved and minimize their sum with respect to the pipe
diameter. The cost minimization is done for the life cycle of the system using a net
present value approach. Some types of heat distribution systems may have a salvage
value, while others will, in fact, have a disposal cost associated with the end of their
useful lifetime. Since these will in general be mild functions of the pipe diameter,
they will not significantly affect the optimal pipe diameter and thus will not be
treated here. With these limitations in mind, our objective function, the total life
cycle cost, becomes
min. Ct = Chl + Cpe + Cpp + Cm&r
(2-1)
where Ct = total system owning and operating cost ($)
Chl = cost of heat losses ($)
Cpe = cost of pumping energy ($)
Cpp = capital costs of pipes and pumps ($)
Cm&r = cost of maintenance and repair ($).
Now let's look at each of the costs in eq 2-1 in detail, starting with the cost of heat
losses.
COST OF HEAT LOSS
The basic form of the heat loss cost is
Chl = PVFh ∫yr ChQhldt
(2-2)
where Ch
= cost of heat ($/Wh)
PVFh
= present value factor for heat (dimensionless)
Qhl
= rate of heat loss (W)
= time of year (hr [0 ≤ t ≤ 8760]).
t
In the most general case, the cost of heat Ch can be a function of time because of
seasonal usage rates. The rate of heat loss Qhl will also be a function of time over the